Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C47×#3266 ⋊ C2 |
| Sylow | C47 ⋊ #61080 |
2742 conjugacy classes of subgroups.
| minimal degree | μ(G) = 67 |
| transitive degree | μt(G) = 3008 |
A minimal faithful permutation representation — 5 generators on 67 points:
(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(52,54)(53,59)(55,62)(56,61)(57,64)(58,65)(60,66)(63,67);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(53,58)(55,63)(57,60)(59,65)(62,67)(64,66);(49,51)(54,61)(59,66)(62,67)(64,65);(52,53,56,60)(54,59,61,66)(55,58,63,57)(62,65,67,64);(48,49)(50,51)(53,57)(54,61)(55,63)(58,60)(59,65)(64,66)Polycyclic presentation:
2^8,47|b^2=h,f^2=h,b^a=bf,c^a=cg,e^a=eh,f^a=fh,d^b=df,f^b=fh,e^c=eh,f^d=fh,i^d=i^46,i^e=i^46719 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1045462);